I started thinking of this from a meme that it turns out originates from YikYak, an app I haven’t thought about since 2016. I saw it in the context of fake dialogue someone had put over a Doctor Who post. One character asks “Is four a lot?” The other responds “Depends on the context. Dollars? No. Murder? Yes.”
There’s a boundary where things become big. In my mind, this got twisted into the following question: is there context where a number is small, but doubling it is large?1
Money
Money is a tricky one because the context changes dramatically. $5 is small, and so is $10. $100 is huge if you’re a kid, but small if you’re an adult. A $25 gift card is nice (I wouldn’t say “small”), but a $50 one isn’t huge (I might say “big”). Thinking about board games: $50 is fairly standard pricing for large board games. But a lot of gams cost $100 (or even more!). And there’s a ton of games you can pick up under $25.
Thinking even bigger: $10,000 is a huge amount to owe, and $20,000 doesn’t really change the scope of it. $5,000 may be cheap for a major home repair (new roof or air conditioning) but I wouldn’t call it small.2
Money has too many contexts to be reasonable.
I went on a number of different tangent here, false starts and dead ends before I found two areas where I feel like the boundary exist.
Basically, I wanted to find a place where the amount of “big” was clear, take big - 1 or big - 2, hoping it was clearly “small”, and double it to find an obviously big number. Unfortunately, I found a lot of areas where the boundary was nebulous enough that big - 1 was still sort of big-ish.
Obviously, the bigger a number is, the more profound an effect doubling it has. So the domains that work best are ones where either big numbers can still be small, or small numbers can still be big. I apologize for that previous sentence, but I stand by the message.3
Hot dog aside
How much does a hot dog cost? It depends! Anywhere from $1.50 at Costco to about $8 at a baseball game or “fancy”4 restaurant. We can all agree that $10 is expensive for a hot dog, but that doesn’t make $5 cheap.
I found the same hot dog conundrum (which clever readers will recognize is STILL THE SAME MONEY EXAMPLE AS BEFORE — I promise I had other non-money examples that I tested before I wrote this) in many other fields.
Driving Speed
A road near me has a speed of 35 miles/hour. Going 30 on it is, by definition, slow. Going 60 on it is way too fast! That’s a clear marker!5
Dogs and Children
Full credit to my friend Rachel here who pointed out that 2 dogs is not a lot of dogs, but 4 dogs is a ton of dogs. My wife pointed out that the logical extrapolation was to children, but there was some disagreement about whether 3 children counted as a lot (note: we have three children).
Bonus: time again
As I write this, I consider song length. 2 minutes 30 seconds is a short song, 5 minutes would be considered a long song by most modern audiences. I think you could get away with saying that 3 minutes flat is still short, and 6 minutes flat is long.
Conclusion I
Categories are made for man, and do not exist in nature. “Big” is a specific type of category that depends heavily on context. Many households in America own 2 cars. Few (suburban Americans) would consider 3 cars a lot. Everyone I know would consider 6 cars a lot. That’s one domain where the boundary seems really clear6.
A Descent into more nebulous categories
I find the conclusion above unsatisfying, so here are some explorations into domains that don’t have clear boundaries.
Tattoos
Is 2 a lot of tattoos? Not really. Is 4? I guess? I think “a lot of tattoos” is more a function of percent covered available area, since there isn’t a standard size of tattoo. And it’s much harder to think in (or double) percents meaningfully.
Objects some people collect
I considered looking at the number of possessions. Is 20 a lot of DVDs to own? Today, it’s mildly surprising, but it’s not a lot. 15 years ago, it would have been a common, perhaps even low number. 100 seems like a lot, but 50 also does.
Books are even harder, as houses with more than 20 books probably have more than 100.
What about computers? It’s not weird to have one computer. It’s a little weird to have 5. But 3 also feels like a lot.
Phones? 1 is normal, 2 is a bit odd, but not unusual (one for work, perhaps). 4 seems indefensible, but 3 is also pretty odd! I would say that 4 is a large number of phones, but 2 isn’t really a small number.
Conclusion II
Everything here is colored by culture. I know a Londoner who would physically recoil at the sentence I wrote about American suburbanites seeing 2-car households as normal.
I’m not trying to make a grand point here, but I am reminded of the precision principle in Non-Violent Communication. Don’t say “Bob scores a low number of goals”, say “Bob has scored 2 goals over the last 30 games.” This is fact, the former is labelling. If the league average is 20 goals, then Bob is below average. If Bob is the goalkeeper, then 2 goals over 30 games feels like a lot!.
At some point, numbers get big. Where that point is will be different for you and for me. When I was 10, $20 was lifechanging. Today, I can’t tell you exactly how many twenties I have in my wallet. Probably 3? If there’s anything to take away from this, it’s just that you don’t always know context. Consider that, and default to compassion where possible.
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when I was about 8 years old, I was given a time out for 5 minutes. My sister told me “that’s not very long at all”. I refused, and it was lengthened to 10 minutes, which my sister told me was “quite long indeed”7 This experience has clearly stuck with me, and the concept of doubling to become large rattles around my brain like a shaken paint can. ↩
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I remember a saying along the lines of “$1000 is a lot of money to owe, but not a lot of money to have”. It seems fitting that as I write this I have no idea if $1000 was the amount mentioned int he original quote. ↩
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Because I value communicating clearly, I’ll elaborate: a small number being big would be like murders, where 2 is a LOT of murders. A big number being small would be peanuts, rice, or beads, where 100 peanuts isn’t all that much. ↩
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I mean not THAT fancy if they’re serving hot dogs. ↩
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I have only been pulled over twice in my life, both within 5 minutes of each other. I’ll share that story here one day, but the relevant part is this: the second time I was pulled over, the cop said “Can you believe I caught you going 72?” I had just passed a sign telling me the speed limit was 70, so I gave a long, drawn out, “Yees?”, thinking to myself man, are we really doing this?. It turns out, the speed limit was actually 55 for the weekend (Sturges motorcycle convention in North Dakota), so the officer and I had very different expectations of what “fast” meant. I did not get a ticket. ↩
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I promise that before I wrote this blog, I had dozens of examples spinning around my head for weeks where the answer was nebulous. Now they are gone, replaced by the clinical, clear-cut contexts where big is a bright, shining line. ↩
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These were almost certainly not her words. ↩